I suggest that you contact Tokina
directly to find out what range of temperatures your lens is designed to work across.
Your expression "cold weather" is an imprecise term; where I am in the UK means at worst down to a few degrees below freezing and usually a bit above, but when I'm in Moscow they don't consider it to be cold until the temperature drops to around minus twenty-five Celsius.
Depending on where you are, your lens may simply be unable to cope with what you describe as cold weather but you won't know until you have the specifications from Tokina
. If it turns out that your lens is not performing as intended, then the manufacturer will be able to suggest remedies to you.
Sorry I cannot be more specific but Tokina do not appear to have published the range of operating temperatures in the public domain.